Refining Weak Turbulence Models for Intermittent Systems Using Non-Gaussian Corrections

In toroidal ion temperature gradient (ITG) driven turbulence, the heat flux remains suppressed beyond the threshold of linear instability. This phenomenon is known as the Dimits shift. It occurs because zonal flows regulate turbulence and reduce thermal energy transport by catalyzing resonant nonlinear energy transfer from unstable to stable modes. To study turbulence, many traditional closure models assume that it follows quasi-normal statistics. However, real plasma turbulence often behaves unpredictably, and turbulence in the Dimits regime exhibits strongly non-Gaussian characteristics. Therefore, it is important to consider the impact of heavy tailed distributions and excess kurtosis when analyzing energy transport. The primary goal of this project is to investigate these appreciably non-Gaussian statistical features in the Dimits regime. Previous studies have found a resonance term in the fourth-order cumulant growth rate that is associated with the kurtosis of the fluctuation probability distribution. In this work, we refine a prior weak turbulence closure calculation for zonal flow Fourier-autocorrelation by incorporating these kurtosis-based resonances, which are found at higher order in perturbation than previously considered. These corrections allow for a simple parameterization of the influence of a heavy tail on the statistics. Our analytic analysis is complemented by the results of numerical simulations of a reduced two-field fluid model for toroidal ITG turbulence.